For a critical value or a threshold to be useful in finite sample,
their selection requires the estimation of the level of noise,
such as the error variance \(\sigma ^2 = \mathsf {Var}(\varepsilon _t)\)  under independence
or the long-run variance \(\tau ^2 = \mathsf {Var}(\varepsilon _t) + 2 \sum _{h = 1}^\infty \mathsf {Cov}(\varepsilon _0, \varepsilon _h)\) 
when serial dependence is permitted.
Several estimators exist for both \(\sigma ^2\)  and \(\tau ^2\) 
under the model (REF ) [1]}, [2]}, [3]}, [4]},
but the difficulty associated with the estimation of the latter
has been well-documented particularly in the presence of multiple change points [5]},
and the former also becomes challenging to estimate when frequent change points are present.
As a remedy, [6]} proposes the
`steepest drop to low levels' (SDLL) model selection methodology
applicable with a complete solution path ordering \(\mathcal {I}_1 = \lbrace 1, \ldots , n - 1\rbrace \) ,
where thresholding is adopted as a secondary criterion.
